OR 674/SYST 674Dynamic Programming (Graduate) for Fall 2014

Pre Req: OR 442 or OR542 or Permission of Instructor

Instructor: Rajesh Ganesan, Ph.D.

703-993-1693

ENGR 2217 Office Hrs: MW 2-3 PM

Course Description:

This is a course on the theory and practice of dynamic programming, i.e. optimal sequential decision making over time in the presence of uncertainties. The course will stress intuition, the mathematical foundations being for the most part elementary. It will introduce the theory, applications (finance, engineering, and biology), and computational aspects of dynamic programming for deterministic and stochastic problems. The course will use some Matlab and spread sheets to solve DP problems, however prior knowledge of Matlab or spread sheet use is not needed.

Course Objectives:

At the conclusion of this course the student will have learned the art of formulating recursive equations, and how and why dynamic programming is the only method that can solve many of the large scale optimization problems involving sequential decision making. The student will also have advanced knowledge of solving optimization problems that involve sequential decision making in both deterministic and stochastic environment.

The field of dynamic programming provides alternate approaches to solving many optimization and control problems. Large scale optimization and control has become very important in recent years, which involve complexity and are often model free. Also adaptive systems with sequential decision making powers are sought after for effective real time optimization and control. The above is achievable only via dynamic programming, which is often solved using artificial intelligence (stochastic approximation methods). Many large scale industrial and defense applications such as airline pricing, optimal power flow, helicopter control, and missile control use approximate dynamic programming approaches, which has created a demand for this knowledge.

This is a new course in the SEOR program that has been designed to provide a wealth of knowledge that is directly applicable to the needs of applications that are complex, adaptable, and large scale. The course compliments the fundamentals learnt in OR441/OR541 and OR442/OR542 and introduces a new and powerful alternate method to solve many optimization problems that involve sequential decision making.

Text: Eric Denardo, Dynamic Programming: Models and Applications,Dover, May 2003.

Problems from Operations Research by Winston. W. L. (Chapters 18 and 19). This book is the same book that you have used for OR 541 and OR 542.

Notes from References Books

  • Applied Probability and Stochastic Processes by Feldman & C. Valdez-Flores
  • Introduction to Mathematical Programming : Applications and Algorithms Wayne L. Winston, Munirpallam Venkataramanan
  • Approximate Dynamic Programming: Warren Powell.
  • Dynamic Programming by Richard Bellman
  • Dynamic Programming and Optimal Control (Volumes 1 and 2) by Dimitri P. Bertsekas
  • Introduction to Stochastic Dynamic Programming by Sheldon M. Ross
  • Neuro-Dynamic Programming (Optimization and Neural Computation Series, 3) by Dimitri P. Bertsekas, John N. Tsitsiklis
  • Markov Decision Processes: Discrete Stochastic Dynamic Programming by Martin L. Puterman

Deterministic Dynamic Programming:

Week 1Course introduction, Finite Decision Trees

Week 2Dynamic Programming Networks and the Principle of Optimality

Week 3 Formulating dynamic programming recursions, Shortest Path Algorithms, Critical Path Method, Resource Allocation (including Investments)

Week 4Knapsack Problems, Production Control, Capacity Expansion, and Equipment Replacement

Week 5Infinite Horizon Optimization including Equipment Replacement over an Unbounded Horizon

Weak 6 Infinite Decision Trees and Dynamic Programming Networks

Week 7 Midterm

Stochastic Dynamic Programming

Week 8 Stochastic Shortest Path Problems with examples in Inventory Control

Week 9Markov Decision Processes, value and policy iteration for average cost criteria

Week 10Markov Decision Processes, value and policy iteration for discounted cost criteria

Week 11Markov Decision Processes, value and policy iteration for discounted cost criteria

Week 12MDP with examples in Equipment Replacement and inventory problems

Week 13Semi-Markov Decision Process

Week 14Semi-Markov Decision Process

Week 15Final exam (exam week)

Student Evaluation Criteria
Mid-term:40%

Project:20%(Due on Dec 10th)

Final Exam:40% (Due on Dec 10th)

Academic Policy:

All academic policies as given in the Honor System and code will be strictly followed. Visit URL

Grades:

Letter grades will be decided as follows:

97% and above –A+, 94-96%- A, 90-93% -A-, 86-89- B+, 83-85%-B, 80-82%-B-, 76-79%- C+, 73-75%- C, 70-72%-C-, 66-69%-D+, 63-65%-D, 60-62%-D-, at or below 59%-F

Class Website: For final grades check patriotweb